﻿854 
  Mr. 
  F. 
  Soddj 
  on 
  the 
  

  

  was 
  almost 
  too 
  small 
  to 
  be 
  within 
  the 
  range 
  of 
  the 
  older 
  

   methods. 
  In 
  Experiment 
  IV. 
  no 
  initial 
  measurements 
  were 
  

   taken. 
  In 
  the 
  older 
  tests 
  a 
  brass 
  electroscope 
  had 
  been 
  used, 
  

   and 
  this 
  was 
  calibrated 
  at 
  every 
  test 
  with 
  reference 
  to 
  a 
  

   7-ray 
  radium 
  standard. 
  As 
  was 
  pointed 
  out 
  (II. 
  p. 
  286) 
  the 
  

   measurements 
  so 
  corrected 
  were 
  not 
  nearly 
  so 
  regular 
  as 
  the 
  

   actual 
  observations. 
  In 
  light 
  of 
  recent 
  results 
  on 
  the 
  un- 
  

   certainty 
  attaching 
  to 
  7-ray 
  measurements, 
  it 
  is 
  best 
  to 
  reject 
  

   these 
  calibration 
  tests 
  altogether 
  and 
  to 
  assume 
  that 
  the 
  

   sensitiveness 
  of 
  the 
  electroscope 
  did 
  not 
  vary. 
  Recalculating 
  

   from 
  the 
  table 
  (II. 
  p. 
  282) 
  gives, 
  according 
  to 
  present 
  data, 
  

   the 
  value 
  12 
  for 
  the 
  constant 
  of. 
  the 
  instrument. 
  The 
  mean 
  

   of 
  the 
  first 
  nine 
  tests 
  over 
  the 
  first 
  309 
  days 
  given 
  in 
  the 
  

   table 
  (II. 
  p. 
  286) 
  recalculated 
  gives 
  the 
  initial 
  quantity 
  of 
  

   radium 
  as 
  15-8 
  units. 
  The 
  initial 
  quantity 
  indicated 
  by 
  the 
  

   curve 
  on 
  the 
  assumption 
  that 
  the 
  rate 
  of 
  production 
  in 
  terms 
  

   of 
  the 
  square 
  of 
  the 
  time 
  has 
  been 
  constant 
  from 
  the 
  start, 
  

   is 
  about 
  12*5 
  units. 
  This 
  evidence 
  so 
  far 
  as 
  it 
  goes 
  thus 
  

   bears 
  out 
  the 
  view 
  that 
  new 
  short-lived 
  intermediate 
  bodies 
  

   exist. 
  

  

  VI. 
  llie 
  Effects 
  of 
  Short-lived 
  Intermediate 
  Products. 
  

  

  The 
  general 
  effects 
  of 
  short-lived 
  intermediate 
  bodies 
  may 
  

   now 
  be 
  considered. 
  Let 
  A, 
  B, 
  C, 
  D, 
  E 
  ... 
  and 
  Xi, 
  Xg, 
  X3, 
  

   X4, 
  X5 
  . 
  . 
  . 
  denote 
  the 
  quantities 
  and 
  radioactive 
  constants 
  

   respectively 
  of 
  a 
  parent 
  element 
  and 
  its 
  successive 
  products. 
  

   It 
  is 
  assumed 
  that 
  initially 
  the 
  products 
  are 
  absent, 
  and 
  that 
  

   the 
  change 
  of 
  the 
  parent 
  is 
  so 
  slow 
  that 
  its 
  quantity 
  ma.y 
  be 
  

   considered 
  constant. 
  The 
  ditferential 
  equations 
  connecting 
  

   the 
  terms 
  are 
  

  

  f=X3C-[X,D];f 
  = 
  X.D-[X.E]. 
  

  

  If 
  we 
  assume 
  that 
  the 
  periods 
  of 
  the 
  first 
  two 
  products, 
  

   B 
  and 
  C, 
  are 
  short 
  and 
  those 
  of 
  the 
  others 
  long 
  the 
  terms 
  in 
  

   square 
  brackets 
  may 
  be 
  neglected. 
  The 
  case 
  then 
  corresponds 
  

   to 
  the 
  disintegration 
  series 
  Uranium 
  ^^ 
  Uranium 
  X 
  -* 
  

   *' 
  Uranium 
  A^'^^ 
  Parent 
  of 
  Radium 
  —* 
  Radium, 
  where 
  

   B 
  denotes 
  uranium 
  X, 
  for 
  which 
  A2 
  ^*s 
  about 
  11*4 
  (year)"^, 
  

   C 
  the 
  suspected 
  new 
  intermediate 
  body 
  " 
  uranium 
  A/^ 
  for 
  

   which 
  the 
  period 
  is 
  probably 
  of 
  the 
  order 
  of 
  unity, 
  D 
  the 
  

   direct 
  parent 
  of 
  radium, 
  and 
  E 
  radium. 
  

  

  